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Year 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers

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Year 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers

Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.

1.For the geometric sequence 4, 16, 64, 256, …, write the common ratio and the rule for the nth term.

Answer: r = 4; Tₙ = 4 × 4n − 1

  1. r = 16 ÷ 4 = 4
2.Find the 23th term of the arithmetic sequence 19, 17, 15, 13, …

Answer: −25

  1. a = 19, d = −2
  2. T23 = 19 + 22 × −2 = −25
3.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.

Answer: r = 5; Tₙ = −2 × 5n − 1

  1. r = −10 ÷ (−2) = 5
4.Find the sum of the first 11 terms of the arithmetic sequence 14, 15, 16, 17, …

Answer: 209

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 11/2 × (2 × 14 + 10 × 1)
  3. = 209
5.For the geometric sequence −4, −16, −64, −256, …, write the common ratio and the rule for the nth term.

Answer: r = 4; Tₙ = −4 × 4n − 1

  1. r = −16 ÷ (−4) = 4
6.Find the sum of the first 11 terms of the arithmetic sequence 15, 16, 17, 18, …

Answer: 220

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 11/2 × (2 × 15 + 10 × 1)
  3. = 220
7.Find the 17th term of the arithmetic sequence 1, −5, −11, −17, …

Answer: −95

  1. a = 1, d = −6
  2. T17 = 1 + 16 × −6 = −95
8.For the geometric sequence 2, 10, 50, 250, …, write the common ratio and the rule for the nth term.

Answer: r = 5; Tₙ = 2 × 5n − 1

  1. r = 10 ÷ 2 = 5
9.Find the 19th term of the arithmetic sequence 7, 11, 15, 19, …

Answer: 79

  1. a = 7, d = 4
  2. T19 = 7 + 18 × 4 = 79
10.Find the 7th term of the geometric sequence 3, 12, 48, 192, …

Answer: 12288

  1. a = 3, r = 4
  2. T7 = 3 × 46 = 12288
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